Investigating zero transmission of HIV in the MSM population: a UK modelling case study

Background UNAIDS 90-90-90 goals for HIV have been surpassed in the UK, with focus now moving to ending transmission by 2030. The concept of zero transmission is complex and many factors can influence transmission. We aimed to investigate how the target of zero transmission might be reached in the UK. Methods We developed a de novo Markov state transition open cohort model of HIV with a 50-year time horizon, which models six key screening, treatment and prevention parameters, including treatment-as-prevention (TasP) and pre-exposure prophylaxis (PrEP). We studied the anticipated HIV epidemic trajectory over time in men who have sex with men (MSM), with and without changing the six key parameters, defining zero transmission as a 60% reduction in incidence compared with 2010 incidence. Results Zero transmission in the MSM population was not achieved within the model’s time horizon in our base case scenario, when the six key parameters were set to their 2019 values. Several future scenarios were explored, including a combination approach to preventing HIV transmission through increasing five key parameter values and considering three different TasP values; zero transmission was achieved by 2030 in the scenario where TasP was increased from its current level of 97–99%, avoiding 48,969 new HIV cases over the time horizon and reducing the lifetime risk of acquiring HIV for HIV-negative MSM not using PrEP from 13.65 to 7.53%. Conclusions Zero transmission in the UK MSM population can be reached by the target year of 2030 with bold changes to HIV policy. A combination approach such as the UK Government’s ‘Towards Zero’ Action plan, impacting multiple policies and including an increase in TasP, has the potential to achieve meaningful reductions in HIV transmission and meet this ambitious goal. Supplementary Information The online version contains supplementary material available at 10.1186/s13690-023-01178-0.


Model structure
The structure of the Zero Transmission Model is shown in Figure 1 of the main text.
The health states illustrated represent the possible 'status' of individuals in the model at any time: individuals can be HIV -positive or -negative, diagnosed or undiagnosed, on treatment or not on treatment, virologically suppressed or unsuppressed.
Additionally, HIV-negative men who have sex with men (MSM) are subdivided based on whether they are receiving PrEP.Further, MSM living with HIV (MSMLWH) who are not diagnosed, and MSMLWH who are diagnosed but not on treatment (red and blue boxes, respectively, in Figure 1) are distributed across four health states depending on their CD4 cell count.This allows the model to track the natural progression of the disease if individuals are not treated.MSMLWH who are receiving treatment for HIV are subdivided based on whether they are virologically suppressed or not.On-treatment individuals are assumed to have stable CD4 cell counts over time; individuals who are virologically suppressed are assumed to have a CD4 cell count of >500 cells/mm 3 and individuals who are unsuppressed are assumed to have a CD4 cell count of <200 cells/mm 3 .
At each model cycle, HIV-negative MSM not using pre-exposure prophylaxis (PrEP) have both a chance of acquiring HIV and of starting PrEP.Individuals who are 'HIVnegative (on PrEP)' have reduced susceptibility to HIV transmission, based on the efficacy of PrEP.As MSM who are using PrEP are monitored closely and tested regularly for HIV, it is assumed that all MSM who acquired HIV while using PrEP will be diagnosed within three months of transmission (termed the acute phase, a health state lasting for one cycle), whilst in the 'acute phase (on PrEP)' health state.

HIV Transmission
PrEP and ART both reduce HIV transmission.Within the model, the number of individuals who have adopted each of these measures, and their effectiveness, reduces the number of new transmissions each cycle.
• The 'HIV-negative, on PrEP' population has a reduced risk of acquiring HIV (compared with the 'HIV-negative, not on PrEP' population) due to the efficacy of PrEP.PrEP relative reduction in incidence is set to 86% in the model.(4) • ART reduces an individual's viral load to undetectable levels, which prevents them from transmitting the virus.For individuals who are on ART and suppressed, the reduction in viral transmission due to ART is assumed to be 100%.For simplicity, individuals who are unsuppressed were assumed to be to transmit the virus as readily as individuals not receiving ART.
PrEP and ART effectiveness, and the number of individuals who have adopted these measures, were directly considered in the formula used within the model for calculating the number of new infections that occur each cycle: Where: • n is the number of people in a given group, • inf, no ART is infected not on treatment, and unsuppressed ART MSMLWH, • inf, ART is HIV-positive, on treatment and suppressed, • not inf, no PrEP is HIV-negative MSM not receiving PrEP, • not inf, PrEP is HIV-negative MSM on PrEP, • RR_ART is the relative risk of transmission of persons on ART and suppressed vs. other persons, • RR_PrEP is the relative HIV transmission susceptibility of persons on PrEP vs.
other persons, • Total popn is the number of the total model population (currently alive), • β is an estimate of the basic reproduction number, that is the number of new HIV cases generated by one MSMLWH (each cycle), if the entire population was susceptible to transmission.The other inputs listed above were employed in the formula to adjust the β factor to take into account the effectiveness of PrEP and ART (which reduce this susceptibility) and the number of individuals that have adopted each measure.Based on the available data, estimating β by rearranging the equation above was deemed the most appropriate approach.
The initial β in the model, i.e. for 2020, was calculated as the average of the computed βs for the years 2012-2018.For each of these years, β was calculated using the same formula described above (rearranged), employing PHE historical data on total MSM population, HIV incidence and prevalence, and the number of MSM Footnotes: BASHH: British Association for Sexual Health and HIV; MSM: men who have sex with men; N/A: not applicable; ONS: Office for National Statistics.

Implementing changes to epidemiology inputs
For key, user-adjustable input parameters, changes are implemented linearly between 2020 to 2024, except for the rate of PrEP uptake, for which changes were implemented linearly between 2020 and 2022.This difference in the rate of parameter change aims to reflect the current status of HIV policy in the UK.The slower increase in rate of screening, time to treatment and TasP parameters aims to reflect the 'lag time' which might be experienced following the implementation of policy change, between the change in policy and full implementation and uptake.In contrast, given that PrEP is now available on the NHS and the level of awareness of PrEP in the MSM community, it is anticipated that PrEP uptake will occur more quickly than other parameters.

Disease progression inputs
Supplementary Table 3 and Supplementary

Transition probabilities
The inputs described previously, plus published data on HIV progression and mortality, informed the probabilities employed in the model (converted as explained above, when needed).
For mortality: • HIV mortality data by CD4 count (20) informed the chance of moving to the "death" health state from each of these CD4-related health states, regardless of whether individuals in that CD4 count health state are diagnosed or not.
• MSMLWH on treatment who achieved virological suppression had the same chance of dying as HIV-negative MSM (i.e.baseline mortality).Risk of death depends on age such that HIV-negative MSM have a slightly lower rate of death overall than virologically suppressed MSMLWH.
• MSMLWH on treatment who did not achieve virological suppression had the same chance of dying as people diagnosed with AIDS.
For HIV progression: • The HIV progression probabilities from Mangal et al., 2017(20) informed the transition of diagnosed and undiagnosed MSMLWH to health states with a lower CD4 count, unless they were already CD4<200 (and unless they were diagnosed/started treatment, in which case they transitioned to the corresponding diagnosed/on treatment health states).

Key assumptions
This model is by nature a simplification of the real world.Several assumptions have been made in the model, for example due to insufficient data being available for parameters.The following key modelling assumption was externally validated: • HIV testing is 100% accurate, with all HIV-positive MSM being diagnosed upon screening.This is a reasonable assumption as fourth generation pointof-care blood tests are standard in the UK and have 99•99% sensitivity and specificity across all subgroups, and all positive HIV tests are followed up with a confirmatory second test to provide diagnostic certainty.

A
proportion of MSMLWH are diagnosed in the 'acute phase' health state, representing the proportion of individuals who are diagnosed within three months of transmission.If not diagnosed in the acute phase, MSMLWH enter the 'HIV-positive and undiagnosed' state, in which they progress through successive CD4 cell count states until they are diagnosed.Individuals who reached the CD4<200 state are diagnosed in the next cycle, as they are detected through their presentation with AIDS-defining illnesses.(1)This assumption was taken from a modelling study in which the model was calibrated against data from a clinical study in Hackney, UK.(1)When fitting their model, Baggaley et al. (2017) found that values were equivalent to almost instantaneous diagnosis and interpreted as reflecting rapid diagnosis due to high levels of symptomatic presentations.(1)A proportion of MSMLWH in each undiagnosed health state are diagnosed each cycle, based on the key model variables and model inputs for HIV testing rates.A proportion of these diagnosed individuals move directly to the 'diagnosed and on treatment' state, representative of individuals who start antiretroviral therapy (ART) within three months of their diagnosis.The remainder of the MSMLWH move to the 'diagnosed and not on treatment' state, where they continued to progress through CD4 cell count states until they initiate treatment.At the end of each cycle, 'diagnosed and not on treatment' MSMLWH have a chance to move to one of the 'on treatment' health states.Individuals that are on treatment are distributed across the 'on treatment and suppressed' and the 'on treatment and unsuppressed' health states every cycle.At the end of every cycle there is a chance that individuals will die, based on the mortality rate associated with their current health state.New MSM and MSMLWH enter the model each cycle in line with population growth estimates from the Office of National Statistics (ONS).(2)These individuals are distributed across all health states according to the population distribution of the initial model cycle, accounting for the fact that some cases of HIV are known to be acquired outside of the UK.(3) using ART and PrEP.The initial β was used to calculate the number of new transmissions on the second cycle of the model.The estimated number of new transmissions was then used to calculate the β in the following cycle, and so on.
because younger people (<35 years old) are less likely to acquire HIV, while people living with HIV are living relatively normal, long lives.It is assumed that this observation around the general population of PLWH also applies to MSMLWH.This was reflected in the model by including a higher median age for MSMLWH, which increased more quickly than the HIV-negative MSM population over time.

Table 3 . Hazard ratio for age inputs
Table 4 outline the disease progression and mortality probabilities used in the model.